A fast algorithm for generating set partitions
The Computer Journal
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Regular Article: Necklaces, MSS Sequences, and DNA Sequences
Advances in Applied Mathematics
Generating Bracelets in Constant Amortized Time
SIAM Journal on Computing
A Filtering Algorithm for the Stretch Constraint
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Breaking Row and Column Symmetries in Matrix Models
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
A fast algorithm to generate necklaces with fixed content
Theoretical Computer Science
Symmetry Breaking using Value Precedence
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Solving Necklace Constraint Problems
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
An efficient way of breaking value symmetries
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
General symmetry breaking constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Static and dynamic structural symmetry breaking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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Some constraint problems have a combinatorial structure where the constraints allow the sequence of variables to be rotated (necklaces), if not also the domain values to be permuted (unlabelled necklaces), without getting an essentially different solution. We bring together the fields of combinatorial enumeration, where efficient algorithms have been designed for (special cases of) some of these combinatorial objects, and constraint programming, where the requisite symmetry breaking has at best been done statically so far. We design the first search procedure and identify the first symmetry-breaking constraints for the general case of unlabelled necklaces. Further, we compare dynamic and static symmetry breaking on real-life scheduling problems featuring (unlabelled) necklaces.